How to move a bone in pose mode using python?
Pose bones belong to the object

If ob is our armature object, ob.type == 'ARMATURE' the pose bones belong to ob.pose.bones.  The edit bones are in the armature ob.data.bones.

To set active pose bone(s) to use operators see Set active bone in pose mode from Python script

To get a specific pose bone knowing its name

name = "Bone"
pb = ob.pose.bones.get(name) # None if no bone named name


Once you have the pose bone can set its properties or matrix.  

pb.location = (0, 0, 1)


How to get world-space matrix of any pose bone?

Add keyframe for all locations x, y, z at frame 23

pb.keyframe_insert("location", frame=23)


Note if a bone is connected then translating will have no effect.